Most building materials are manufactured in flat, straight or extruded pieces. The components of buildings are mostly constructed to be level with either a horizontal or vertical plane having flat surfaces with boxed, square or rectangular forms.
When a curved surface or finish is required in a structure it is achieved either by a complex and expensive method of bending the available traditionally straight materials or making the curved surface from many smaller components fixed at an angle to each other. To make a dome or a complex arched or vaulted surface in three dimensions, the process is even more complicated. The form is generally achieved by making a temporary form or mould into which material such as concrete is poured to create the structure. This is extremely labour intensive, complex and prohibitive from an economic viewpoint. This is generally why curved surfaces are rare in constructed buildings.
Furthermore, building materials such as thin sheets can generally be curved or bent into a cylinder shape, that is, along one axis such as the x axis. The same sheet could also be independently bent along the y axis but bending over both the x and y axis at the same time to form a portion of a sphere or a dome is normally not possible. Unless specially treated with heat and pressure in a mould, materials such as plasterboard, sheet aluminium, sheet steel, plastic or particleboard or the like cannot be deformed simultaneously in two or even three planes.
Currently the bending of these materials is problematic and often requires a solid permanent framework to hold the desired curves in shape. The framework is also complex and is often made up of segments of straight material.